Understanding Free Modes in Simple Harmonic Oscillators

Thread starter physicsjock
Start date Jan 23, 2012
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Harmonic Harmonic oscillator Oscillator Simple harmonic oscillator

In summary, a simple harmonic oscillator is a system that follows a specific pattern of motion where the force is directly proportional to the displacement and directed towards the equilibrium point. Some real-life examples include pendulums, mass-spring systems, and guitar strings. The period of a simple harmonic oscillator is affected by the mass and spring constant, with an increase in mass or decrease in spring constant resulting in a longer period. The displacement of a simple harmonic oscillator can be represented by the equation x = A cos(ωt + φ), where A is the amplitude, ω is the angular frequency, and φ is the phase angle. The total energy of a simple harmonic oscillator is directly proportional to the square of the amplitude, meaning that increasing the amplitude

Jan 23, 2012

physicsjock

In the context of normal modes, what is a free mode?

When the whole system is in motion?

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Jan 23, 2012

ehild

Homework Helper

I think free mode of vibration means an unforced vibration, without external forces.

ehild

Last edited: Jan 23, 2012

1. What is a simple harmonic oscillator?

A simple harmonic oscillator is a type of system that follows a specific pattern of motion, where the force acting on the system is directly proportional to the displacement from the equilibrium point and is always directed towards the equilibrium point.

2. What are some real-life examples of simple harmonic oscillators?

Some common examples of simple harmonic oscillators include pendulums, mass-spring systems, and guitar strings.

3. How does the period of a simple harmonic oscillator change with different mass and spring constant?

The period of a simple harmonic oscillator is directly proportional to the square root of the mass and inversely proportional to the square root of the spring constant. This means that increasing the mass or decreasing the spring constant will result in a longer period, and vice versa.

4. What is the equation for the displacement of a simple harmonic oscillator?

The displacement of a simple harmonic oscillator can be represented by the equation x = A cos(ωt + φ), where A is the amplitude, ω is the angular frequency, and φ is the phase angle.

5. What is the relationship between energy and amplitude in a simple harmonic oscillator?

The total energy of a simple harmonic oscillator is directly proportional to the square of the amplitude. This means that increasing the amplitude will result in an increase in energy, and vice versa.